The unit groups of class character rings of Rudvalis group
Čelâbinskij fiziko-matematičeskij žurnal, Tome 2 (2017) no. 2, pp. 133-151.

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In our work we study the class character rings of group $\mathit{Ru}$, which are not the subrings of real quadratic fields. Their units are described.
Keywords: sporadic group, unit, character, group rings, class character ring.
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R. Zh. Aleev; M. I. Molodorich. The unit groups of class character rings of Rudvalis group. Čelâbinskij fiziko-matematičeskij žurnal, Tome 2 (2017) no. 2, pp. 133-151. http://geodesic.mathdoc.fr/item/CHFMJ_2017_2_2_a0/

[1] R.Zh. Aleev, “Central elements of integral group rings”, Algebra and Logic, 39:5 (2000), 293–300 | DOI | MR | Zbl

[2] M.I. Molodorich, “The class character rings of sporadic groups”, Siberian Electronic Mathematical Reports, 11 (2014), 878–886 (In Russ.) | MR | Zbl

[3] M.I. Molodorich, “The unit groups of class character rings of sporadic groups”, Siberian Electronic Mathematical Reports, 13 (2016), 38–48 (In Russ.) | MR | Zbl

[4] R. Zh. Aleev, M. I. Molodorich, “Class character rings of groups $J_1$ and $O'N$”, Groups and Graphs, Algorithms and Automata, Abstracts of the International Conference and PhD Summer School in honor of the 80th Birthday of Professor Vyacheslav A. Belonogov and of the 70th Birthday of Professor Vitaly A. Baransky, 2015, 31

[5] Groups, Algorithms, and Programming, Version 4.8.3, , The GAP Group, GAP (accessed 12.03.2017) http://www.gap-system.org

[6] Z.I. Borevich , I.R. Shafarevich, Number Theory, Academic Press, New York–San Francisco–London, 1966, 435 pp. | MR | MR | Zbl

[7] R.Zh. Aleev , V.S. Taksheeva, “Generators of the group of cyclotomic units”, Bulletin of Chelyabinsk State University, 2008, no. 6 (107), 121–129 (In Russ.) | MR | Zbl

[8] J. M. Masley, “Solution of small class number problems for cyclotomic fields”, Compositio Mathematica, 33:2 (1976), 179–186 | MR | Zbl

[9] W. Narkiewicz, Elementary and Analytic Theory of Algebraic Numbers, PWN — Polish Sci. Publ., Warsaw, 1974, 630 pp. | MR | Zbl

[10] R.Zh. Aleev, “The units of character fields and the central units of integer group rings of finite groups”, Siberian Advances in Mathematics, 11:1 (2001), 1–33 (In Russ.) | MR | Zbl